Tuesday, January 10, 2017

power series for arc [ tan (x) ]

power series for arc [ tan (x) ] in powers of x

power series for inverse function of tan(x)

let y  = arc [ tan (x) ]

differentiate y with respect to x once to get y' and find y'(0)

then expand the derivative [ 1 + x^2]^ (-1) using  binomial series

now you can differentiate the series as many times as you want and replace x with 0 .

Use the values to substituted into Mc laurin's series or Taylor's series.

mclaurin's power series for ln(1+x) 

approximation of an integral using binomial series

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